Published online 11 July 2012
Nucleic Acids Research, 2012, Vol. 40, No. 18 8803–8817
doi:10.1093/nar/gks600
Crucial role of dynamic linker histone binding
and divalent ions for DNA accessibility and
gene regulation revealed by mesoscale modeling
of oligonucleosomes
Rosana Collepardo-Guevara1 and Tamar Schlick1,2,*
1
Department of Chemistry, New York University, 100 Washington Square East, New York, NY 10003
and 2Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York,
NY 10012, USA
Received March 7, 2012; Revised May 15, 2012; Accepted May 28, 2012
ABSTRACT
Monte Carlo simulations of a mesoscale model of
oligonucleosomes are analyzed to examine the
role of dynamic-linker histone (LH) binding/unbinding in high monovalent salt with divalent ions, and to
further interpret noted chromatin fiber softening by
dynamic LH in monovalent salt conditions. We find
that divalent ions produce a fiber stiffening effect
that competes with, but does not overshadow,
the dramatic softening triggered by dynamic-LH
behavior. Indeed, we find that in typical in vivo
conditions, dynamic-LH binding/unbinding reduces
fiber stiffening dramatically (by a factor of almost 5,
as measured by the elasticity modulus) compared
with rigidly fixed LH, and also the force needed to
initiate chromatin unfolding, making it consistent
with those of molecular motors. Our data also
show that, during unfolding, divalent ions together
with LHs induce linker-DNA bending and DNA–DNA
repulsion screening, which guarantee formation of
heteromorphic superbeads-on-a-string structures
that combine regions of loose and compact fiber
independently of the characteristics of the LH–core
bond. These structures might be important for gene
regulation as they expose regions of the DNA selectively. Dynamic control of LH binding/unbinding,
either globally or locally, in the presence of divalent
ions, might constitute a mechanism for regulation of
gene expression.
INTRODUCTION
Understanding how chromatin fibers fold and unfold as
well as details of their structure and dynamics on a range
of spatial and temporal scales is important for interpreting
fundamental template-directed processes such as DNA
replication, transcription, and repair. Indeed, the tightly
packed complex array of DNA with histone proteins
undergoes continuous chemical modification and
dynamic association of proteins, such as linker histones
(LHs), which control the accessibility of the genetic
material. Together with internal variations, such as the
nucleosome repeat length (NRL) associated with the
basic repeating unit of DNA wrapped around the nucleosome core (147 bp) plus the variable linker-DNA length,
and external factors such as the ionic environment, these
changes determine the shape of the chromatin fiber at different stages of the cell cycle.
Although it is clear that LHs are essential for understanding chromatin compaction (1–3), many questions regarding the structure and behavior of LH, and its role in
gene regulation remain open [for a thorough review, see
(4)]. We have been intrigued by suggestions that the
dynamic binding/unbinding of LHs in vivo (5,6) and
in vitro (7) may function to alter chromatin organization
by generating complex interaction networks that impart
global changes from local rearrangements (5,8–11). Such
networks are plausible because LHs, sandwiched between
entering and exiting linker DNA, lead to LH/linker DNA
association called DNA stems that rigidify chromatin;
conversely, LH dissociation can disrupt these networks
and trigger unfolding rearrangements. Growing evidence
points to a key role for LH dynamic binding during regulation of chromatin structure and gene expression (12);
that is in vivo LH dynamic binding behavior might allow
remodeling factors to bind to temporarily available
nucleosomal sites and induce chromatin structural
changes to either activate or repress genes (13). In fact,
lower H1 mobility, resulting for instance from LH
dephosphorylation, is suggested to maintain chromatin
in a compact structure and shut down gene expression,
*To whom correspondence should be addressed. Tel: +1 212 998 3596; Fax: +1 212 995 4152; Email: schlick@nyu.edu
ß The Author(s) 2012. Published by Oxford University Press.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/
by-nc/3.0), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
8804 Nucleic Acids Research, 2012, Vol. 40, No. 18
while enhanced H1 mobility is linked to undifferentiated
cells that require flexible chromatin to enable transcription
(14); this is consistent with the presence of LHs with lower
mobility causing inhibition of stem cell differentiation (15)
and higher LH mobility observed in pluripotent stem cells
(14). Furthermore, experiments (14,16) and our previous
modeling of chromatin in monovalent salt (17) have linked
increased mobility of LH (e.g. induced by phosphorylation of LH or acetylation of core histones) to facile chromatin fiber opening. Our work (17) also suggested that
fast and slow LH dynamic binding populations, found
simultaneously in vivo (10,18), cooperate to promote chromatin unfolding with selective DNA exposure at low
forces. However, it remains unclear how such local
exchange processes occur and how they affect chromatin
organization and accessibility at physiological ionic conditions (i.e. with divalent ions).
Divalent ions enhance DNA compaction as they bring
linker-DNA segments closer to one another by screening
their electrostatic repulsion (19). Modeling and experiments have revealed that chromatin fibers with both
LHs and magnesium ions adopt a compact heteromorphic
architecture that combines straight and bent DNA linkers
(19). Although it is clear that divalent ions favor structural
variations in compact chromatin, it is unknown what the
combined effects of divalent ions and LH dynamic
binding/unbinding are during chromatin’s fiber opening.
Fiber heteromorphicity in divalent conditions has led us to
speculate that together divalent ions and dynamic-LH
binding/unbinding might serve a fundamental function
for chromatin unfolding: increasing fiber fluidity by
accommodating more easily structural perturbations and
multiple fiber forms.
Recent chromatin applications, by atomic force microscopy (20), optical tweezers (21–25), and magnetic tweezers
(26), measured the fiber’s stretching response using force–
extension curves and provided information on chromatin’s unfolding behavior. Based on optical tweezers experiments of medium-NRL chromatin, the Bustamante group
offered evidence for an irregular zigzag structure stabilized
by nucleosome–nucleosome interactions <7 pN (21,27).
The van Noort group studied chromatin with two different NRLs (short = 167 bp and medium = 197 bp) subject
to stretching at physiological salt with magnesium ions
and suggested that the response of the short-NRL array
is consistent with a zigzag organization, while that of the
medium-NRL arrays supports a solenoid topology (26).
The latter study also showed that the presence of LHs
does not change the stiffness of medium-NRL fibers
when magnesium ions are present.
Here, we develop and apply a computational approach
to simulate dynamic-LH binding/unbinding under
divalent salt conditions (see ‘Materials and Methods’
section) and study the stretching response of single chromatin fibers as a function of LH concentration and
mobility. Our simulation approach is grounded on a
mesoscale model derived from experimental data of the
chromatin fiber and atomistic properties of its components. This model combines different coarse-grained
strategies for the nucleosome core, histone tails, DNA,
and LHs (Figure 1). Such a modeling strategy allows us
Figure 1. Mesoscale model of the basic chromatin building block
including: nucleosome core surface with wrapped DNA modeled as
an irregularly shaped rigid body with uniformly distributed charges;
linker DNA treated using the discrete worm-like chain model; and
histone tails and linker histones coarse-grained as bead models. The
solvent around the oligonucleosome is treated implicitly as a continuum. The screening of electrostatic interactions due to monovalent
ions in solution (0.15 M NaCl) is treated using a Debye–Hückel potential. A low concentration of magnesium ions is considered by a firstorder approximation as developed in (32), by reducing the DNA
bending persistence length and allowing the DNA beads to nearly
touch one another.
to capture the essential physics of the chromatin fiber (like
its electrostatics, DNA and nucleosome mechanics, structural irregularity, and histone-tail flexibility), and at the
same time to reduce the system dimensionality markedly
and sample the chromatin conformational space exhaustively. This approach has been developed, validated against
experiments, and refined over the past few years, as
detailed extensively in (28–34).
Our results suggest a dramatic softening effect of the
chromatin fiber when LHs associate/dissociate dynamically compared with fixed (or static) LH species; this
produces a stretching resistance compatible with unfolding at natural forces of molecular motors. Moreover, the
detailed fiber configurations corresponding to each stage
of the unfolding process reveal that divalent ions favor
transitional states that combine regions of fully stretched
fiber with prominent compact clusters or superbeads.
These unusual ‘superbeads-on-a-string’ forms, observed
experimentally at different cell types (35) or in the
presence of low concentrations of magnesium ions (36),
suggest mechanisms by which intrinsic and external
factors, such as LH binding and divalent ions, lead to
higher order fiber forms. Although related unfolding
arrays emerged in our studies without divalent ions
focusing on two binding/unbinding scenarios for LHs,
the clumps were sparse (17). This work indicates that
divalent ions are necessary to enhance nucleosome-cluster
stability. Thus, LH mobility and divalent ions may introduce a combined regulatory mechanism for gene expression through a localized transient exposure of
chromosomal DNA.
Nucleic Acids Research, 2012, Vol. 40, No. 18 8805
MATERIALS AND METHODS
Because of the intrinsic complexity of the chromatin
fiber in solution (i.e. the many atoms that constitute it,
the multiple time and length scales involved in its
dynamics, and the interplay of factors that intervene in
its structural reorganization), simulating chromatin’s
folding/unfolding represents a grand challenge for bimolecular modelers. On the one hand, the accuracy of atomistic models is desirable to capture the details of the
chemical interactions, but on the other hand an all-atom
study of oligonucleosomes is prohibitive due to the
massive system dimensionality (e.g. a 50-nucleosome
array without solvent already contains >1 million
atoms). Coarse-graining represents one of the only alternatives to model chromatin, and indeed several other
large-scale bimolecular systems [for an excellent review,
see (37)], because it dramatically reduces the system size
by averaging out many effects (e.g. protein/DNA sequence
effects, hydrogen bonding, atomistic fluctuations, and
solvation), while simultaneously maintains the essential
physical and chemical information required to analyze
its structural organization. This dimensionality reduction
is a major advantage as it allows extensive sampling of the
coarse-grained phase space.
Coarse-grained modeling has been useful to complement experimental analyses and help dissect the factors
that control the structure and dynamics of the chromatin
fiber (38). Among the existing chromatin coarse-grained
models, those that treat the DNA and nucleosome by geometric descriptions have provided insight on the physical
properties of the chromatin polymer (27,39–44), while
more realistic approaches based on all-atom studies and/
or experimental data have dissected the influence of LHs,
nucleosome interactions, and ionic environment on chromatin structure (17,19,32–34,45,46).
Indeed, in silico stretching experiments have been
instrumental for analyzing chromatin’s unfolding
behavior and its implications for DNA accessibility
(17,27,40,44,47). In particular, they have shown that chromatin’s unfolding response is consistent with an irregular
zigzag architecture (27), that the persistence length of
medium-NRL fibers is strongly affected by the excluded
volume of the nucleosomes (47), that chromatin is much
more resistant to stretching than to bending (40), that fiber
stiffness decreases with the NRL and increases in the
presence of rigid DNA stems (17,40), and that simulated
conformations aid the analysis of chromatin force extension experiments (17,44). Analytic approaches have also
provided information on the mechanical properties of the
chromatin fiber (48–50). Here, we refine our mesoscale
model of chromatin, which uses different coarse-grained
interpretations for the different oligonucleosome components, to analyze the effect of LH dynamic binding during
force-induced fiber unfolding.
Mesoscale model
Our model has been recently described in detail in (32,34),
and below we summarize the main features of the
strategies used to treat each oligonocleosome element
(Figure 1).
cores: the nucleosome protein core,
excluding histone tails, with wrapped DNA is
modeled as a rigid irregular body with 300 Debye–
Hückel charges uniformly distributed on the nucleosome molecular surface. The charges are optimized
to reproduce the full atom electric field around the
nucleosome core by the discrete surface charge optimization (DiSCO) algorithm (28), which solves the
complete nonlinear Poisson–Boltzmann equation.
. Histone tails: we model the 10 histone tails protruding
out of each core (the N-termini of each H2A, H2B,
H3, and H4, plus the C-termini of each H2A) as
flexible chains of beads (each bead comprises five
amino acids) with the first bead rigidly attached to
the parent core. The stretching and bending flexibility
constants of each tail inter-bead segment are modeled
by harmonic potentials with parameters developed to
mimic their atomistic flexibilities (32). The charges of
the tail beads are also modeled to reproduce the atomistic properties of the amino acids it represents.
. DNA linkers: the DNA that connects consecutive nucleosomes is treated as a chain of spherical beads that
have a salt-dependent charge parameterized using the
Stigter procedure (51). The mechanical properties of
the linker-DNA chains are also considered and
described with the worm-like chain model (52,53).
The equilibrium DNA inter-bead segment is 3 nm
(9 bp), thus to model an NRL of 209 bp, we use
six DNA beads (seven segments) per linker. The
exiting and entering DNA linkers attached to the nucleosome define an angle of 108 , which corresponds
to the 147 DNA bp tightly wound 1.7 times around
the core.
. Linker histones: the LH proteins are modeled based on
rat H1d LH. The family of eukaryotic LH proteins H1
are formed by a globular domain (80 amino acids)
and two highly positively charged (lysine-rich) terminal
tails (a short N-tail of 14 amino acids and a long
C-tail of 100 amino acids) (54). We neglect the short
relatively uncharged N-terminal domain and model the
C-terminal domain by two charged beads, and the
globular domain by a single bead. The LH beads are
placed on the dyad axis of each nucleosome and are
separated by a inter-bead distance of 2.6 nm, as suggested by Bharath et al. (55). Each LH bead is
assigned a Debye–Hückel charge, also optimized with
DiSCO. Here, we have refined our LH model by
introducing moderate bending and stretching flexibility
to the LH beads through semi-stiff harmonic potentials (with stretching and bending constants empirically
set one order of magnitude greater than those
describing histone-tail motion), and by allowing the
LH beads to interact electrostatically with all chromatin components (see Supplementary Material).
Through the ‘LH reorganization’ MC move,
described below, we produce oligonucleosome ensembles with LH beads in optimized positions near the
dyad axis. Dynamic-LH binding/unbinding is
. Nucleosome
8806 Nucleic Acids Research, 2012, Vol. 40, No. 18
accounted for by the new ‘LH on and off’ move
presented below.
. Solvent and ionic environment: the water around the
oligonucleosome is treated implicitly as a continuum.
The screening of electrostatic interactions due to the
presence of monovalent ions in solution (0.15 M NaCl)
is treated using a Debye–Hückel potential (electrostatic screening length of 1.27 nm1) (32) and, as
described above, with the charges on each component
parameterized considering salt-dependent screening. A
low concentration of magnesium ions is considered as
developed in (32), by reducing the DNA bending persistence length (from 50 to 30 nm) and the repulsion
among DNA linkers (DNA–DNA screening length of
2.5 nm1). Note that only the screening length of the
DNA linkers is adjusted because this is a phenomenological approach based on the argument that, within
compact chromatin, divalent ion screening allows
linker DNAs to almost touch each other. The change
in screening length for all interactions due to a low
concentration of magnesium ions in solution is small
(i.e. from 1.27 to 1.31 nm1) and does not modify the
results (32).
To prevent overlap among chromatin components, each
nucleosome charge, linker-DNA bead, histone-tail bead,
and LH bead are assigned an excluded volume. Specific
expressions for the oligonuclesome energy are given in the
Supplementary Material. Furthermore details and all
values of parameters can be found in (17,32,34); in
addition, Supplementary Table S1 provides a list of
model parameters and the appropriate reference where
their values can be found.
Model limitations
In the past years, innovative chromatin coarse-grained
models, considering very different approximations, have
sprouted [for a recent review, see (56)]. Our model can
simulate moderate oligonucleosome sizes (i.e. 12–48 nucleosomes per fiber) and considers, among other
features, the charged and contoured nucleosome surface,
the flexibility of histone tails, and the presence of LH
proteins. At the same time, compromises are made as
follows. First, although our histone-tail treatment considers them as unstructured protein regions, some experiments (57–59) and modeling (60) have suggested the
intermittent presence of local secondary structure motifs
among the nucleosome histone tails. Our tail models have
been parameterized to reproduce the average atomistic
behavior of the tails. Second, we model the histone
protein core plus DNA around it as a rigid entity, and
thus omit the effects of nucleosome unwrapping and
sliding. For chromatin under tension, nucleosome
wrapping/unwrapping might become relevant at low
forces [4.5 pN for no-LH chromatin in monovalent salt
(44)]. Nonetheless, our coarse-grained model is suitable
for capturing structural rearrangements at the level of
whole chromatin fibers, which take place at longer time
scales. Third, as discussed previously (32), our mesoscale
model does not account for charge–charge correlation
effects, specific protein–protein interactions, and
desolvation effects. Although charge correlation effects
become important in systems with highly charged
surfaces and multivalent counterions, an accurate
modeling of these effects requires explicit treatment of
ions and solvent, and is not feasible for the large
oligonucleosome systems studied here. Specific protein–
protein interactions are needed to properly describe
internucleosome interactions, but they are expected to be
relatively weak when compared with the strong electrostatic interactions among chromatin components.
Similarly, the desolvation effects are expected to be negligible in comparison with the electrostatic interactions.
A comprehensive treatment of these effects is not yet
feasible for large oligonucleosomes as it requires a
detailed description of the nucleosome and explicit treatment of the solvent.
Monte Carlo algorithm
We sample oligonucleosome conformations at constant
temperature with five different Monte Carlo (MC)
moves (global pivot, local translation, local rotation, tail
regrowth, and LH reorganization) and one optional move
to account for dynamic-LH binding/unbinding (LH on
and off, described in ‘LH dynamic binding modeling’
below).
. Pivot, translation, and rotation chain moves: the global
pivot move is implemented by randomly choosing one
linker-DNA bead or nucleosome core and a random
axis passing through the chosen component. The
shorter part of the oligonucleosome about this axis is
rotated by an angle chosen from a uniform distribution within [0, 20 ]. The local translation and rotation
moves also select randomly a oligonucleosome chain
component (linker-DNA bead or core) and an axis
passing through it. In the translation move, the component is moved along the axis by a distance sampled
from a uniform distribution within [0, 0.6 nm]. In the
rotation move, the component is rotated about the
axis by an angle sampled from a uniform distribution
in the range [0, 36 ]. All three MC moves are accepted
or rejected based on the Metropolis criterion.
. Tail regrowth move: the tail regrowth move is implemented to sample histone-tail conformations based
on the configurational bias MC method (61,62). The
move randomly selects a histone-tail chain and
regrows it bead-by-bead using the Rosenbluth
scheme (63). To prevent histone-tail beads from
penetrating the nucleosome core, the volume enclosed
within the nucleosome surface is discretized, and any
trial configurations that place the beads within this
volume are rejected automatically.
. LH reorganization move: the LH reorganization move
is implemented by randomly selecting one LH bead
and an axis passing through it, and then translating
the bead along that axis by a distance sampled from a
uniform distribution within [0, 0.3 nm]. As done in the
tail regrowth move, any trial configurations that place
the LH beads within the nucleosome discretized
volume are rejected automatically. The rest of the
Nucleic Acids Research, 2012, Vol. 40, No. 18 8807
trial configurations are
Metropolis criterion.
selected
based
on
the
The pivot, translation, rotation, tail regrowth, and LH
reorganization moves are attempted with probabilities of
0.2, 0.1, 0.1, 0.4, and 0.2, respectively. In simulations that
consider LH dynamic binding, the probabilities for the
pivot, translation, rotation, tail regrowth, LH reorganization, and LH on and off moves are 0.2, 0.1, 0.1, 0.4, 0.1,
and 0.1, respectively.
LH dynamic binding modeling
Modeling LH’s behavior is intricate. In vivo, H1 binds
dynamically to the cores, exchanging continuously
among nucleosomal binding sites (5,6). To approximate
the dynamic-LH binding behavior (5,6), we have developed an MC procedure that allows the LH proteins
to continuously bind and unbind to different cores
during the simulations. This ‘LH on and off move’
proceeds as follows:
(1) One LH–core binding site is selected at random.
(2) If the LH is bound to a core, a trial configuration is
formed by either leaving the LH bound or with a
probability Pd 2 (0, 1), dissociating it and diffusing
it to infinity so that its contribution to the total
energy is zero. If the LH is unbound, the trial configuration is formed by re-associating it to its core
with a probability Pa 2 (0, 1).
(3) The trial configuration is then accepted or rejected
based on the Metropolis criterion.
The values of Pd and Pa describe the dissociationand-diffusion and association probabilities of LH, respectively. They also measure the LH–core binding affinity and
determine the average number of cores that have a LH
bound to them at any given MC step. Throughout the
simulations, each core can be bound to one or zero LH
molecules, and there are always enough LH proteins to
saturate the nucleosome array. Low LH concentrations
thus reflect low LH–core binding affinities.
The two parameters, Pd and Pa are determined by the
LH–core binding affinity but are difficult to obtain experimentally due to the complexity of the chromatin fiber. As
revealed by fluorescent recovery after photobleaching
(FRAP) experiments, the complex and dynamic LH–chromatin interaction is controlled cooperatively by two DNA
binding sites on LH’s globular domain and the C-terminal
tail (10). The role of the N-tail of LH has not been clearly
identified, and the exact mechanism by which LH’s
globular domain and C-tail act during binding is still
under debate. In addition, the binding properties of LH
also depend on many factors, such as the specific subtype
of LH [H1.1 and H1.2 have low affinity, H1.0 and H1.3
moderate affinity, and H1.4 and H1.5 high affinity (64)],
the presence of post-translational modifications of LHs
domains, replacement of core histones by variants, and
the interaction of LH with other chromatin structural
proteins (12). Thus, in this work, we consider a range of
values that span possible binding scenarios (Table 1).
Table 1. LH dynamic binding model parameters and resulting proportion of LH–core bonds and fiber resting length
Case
Pa Pd
Fixed LH
Effective diffusion (very high
affinity): Pa Pd
High affinity: Pa > Pd
Moderate affinity: Pa = Pd
Low affinity: Pa < Pd
No LH
1
1
0
100
49
0.25 80.45 ± 8.09 53
1
1
0.5
0
0.5
1
1
1
%LH–core
bonds ± SD
67.16 ± 9.54
50.29 ± 10.19
33.40 ± 9.64
0
Resting
length (nm)
60
71
73
74
All fibers with LHs were modeled in high monovalent salt and low
concentration of magnesium ions. Fibers without LH were modeled
in high monovalent salt only.
Our MC sampling of oligonucleosome conformations
allows us to extract qualitative structural and mechanistic
information of chromatin’s unfolding process. Clearly,
our MC procedure is statistical and by ‘dynamic
binding’ we mean a non-zero probability of binding and/
or unbinding. The different chromatin conformations in
the resulting equilibrium ensemble have similar numbers
of total LH–core bonds; however, the specific locations of
the bound sites change among the different conformations. The resulting equilibrium ensemble thus mimics
an array of chromatin fibers in which the LH proteins
bind/unbind in a stop-and-go mode (5).
Implementation of fiber stretching
We mimic the extension experiments by fixing the geometric center position of the first nucleosome core to its initial
position and applying a constant force to the last nucleosome in the oligonucleosome chain, as done previously by
Aumann et al. (40). In practice, we add an stretching
energy term (Epull) to the total oligonucleosome energy
(see Supplementary Material); this term is proportional
to the product of the stretching force (Fpull) and the
distance in the z-direction between the geometric centers
of the first (z1) and last (zNc ) nucleosomes, i.e.
Epull ¼ Fpull jzNc z1 j.
Simulation details
Our simulations are performed at 293 K and high monovalent salt concentration (0.15 M of NaCl). Simulations
for fibers with LH (dynamic and fixed) also consider a
low concentration of magnesium ions. Every simulation
set includes 12 trajectories that cover the mean DNA
twist angle and two DNA twist deviations (±12 ) from
the mean twist to mimic natural variations, as done previously (34). Each simulation trajectory was run for up to
50 million MC steps. Convergence of our simulations is
reached well before 45 million MC steps as shown elsewhere (34). For statistical analysis, the last 5 million steps
were used and only conformations spaced by 100 000 steps
were considered. For our initial configurations, we use
representative zigzag equilibrium conformations at zero
pulling force obtained previously in the presence of fixed
LHs and magnesium ions (34).
8808 Nucleic Acids Research, 2012, Vol. 40, No. 18
RESULTS AND DISCUSSION
1.5
(a)
Dramatic effect of dynamic-LH binding on chromatin
fiber’s elasticity
Exploration of various LH dynamic binding scenarios
In Figure 2b, we compare the stretching behavior of chromatin fibers without LH nor magnesium ions, with LHs
and magnesium ions, and with LHs that bind/unbind dynamically with different affinities and magnesium ions;
Supplementary Figure S1 presents additional data for
fibers without LH and with magnesium ions. In Table 1,
we present the values for the association and
dissociation-and-difussion probabilities we use to model
the different binding affinities. Each binding regime
produces chromatin fibers with different average LH–
core bond concentrations. In the table we provide the
resulting LH–core bond concentrations at zero pulling
force; for each combination of probabilities, similar concentrations are obtained at higher forces. The cases of
Pd = 0 and Pa = 0 reproduce fixed-LH (100% LH
bound) and no-LH (0% LH bound) behavior, respectively
(red and blue curves in Figure 2b). Other probability combinations produce ensembles with intermediate concentrations (four other colored curves in Figure 2b). For
example, the probability combination with PaPd (i.e.
Pa = 1 and Pd = 0.25) mimics dynamic-LH chromatin
fibers where LHs exhibit effective diffusion behavior
(10). This means that, following dissociation, rebinding
occurs much faster than diffusion to infinity.
I(k)
0.5
0
0
2
4 6 8 10 12
k − nucl. num.
40
(b)
+LH (fixed) +Mg 2+; 100% LH
35
+LH (dyn) +Mg 2+; ~80% LH
+LH (dyn) +Mg 2+; ~67%LH
30
+LH (dyn) +Mg 2+; ~50% LH
Force (pN)
Using our mesoscale model, we analyze the unfolding
behavior of 24-core 209-bp repeat oligonucleosomes with
one LH permanently attached to each core and with LHs
that are allowed to bind/unbind to their cores with different affinities (as described in Table 1). These simulations
are performed in physiological conditions (high monovalent salt: 0.15 M NaCl, low concentration of magnesium
ions, and room temperature) and are started from
converged zigzag configurations. As reference, we
perform additional simulations of 24-core 209-bp repeat
arrays without LH with monovalent ions only; simulations analyzing the effect of the NRL, different ratios of
fixed LH–core bonds, and two LH/core binding affinities
in monovalent ions only are reported elsewhere (17),
where longer NRLs were shown to soften the fiber and
an interesting mechanism to facilitate controlled fiber unfolding by the simultaneous presence of fast and slow LH
binding pools was described. The 209-bp repeat fiber is
suitable to dissect the role of LH in chromatin unfolding;
experiments (65) and modeling (17,34) have shown that
LH’s compacting and structural effect is strongest for
medium-NRL arrays [medium NRLs range roughly
from 190 to 210 bp (34)]. In addition, the 209-bp repeat
length is common in nature and close to the value of
chicken erythrocyte chromatin used widely in many
studies [(19,21,36)]. The stretching experiment is implemented by fixing the position of the first nucleosome
core and applying a stretching force of up to 40 pN to
the last core (Figure 2a). Such forces mimic cellular constraints exerted by molecular machines [e.g. RNA and
DNA polymerases (66–70)].
1
+LH (dyn) +Mg 2+; ~33% LH
25
−LH −Mg2+; 0% LH
20
15
10
5
0
0
100
200
300
400
500
600
Extension (nm)
Figure 2. Effect of LH dynamic binding in the force–extension
response of 24-core 209-bp repeat oligonucleosomes. (a) Representation
of the force–extension experiment (left) and internucleosome interaction
pattern of our converged zigzag starting conformation characterized by
dominant k ± 2 and moderate k ± 5 interactions (right). (b) Force–
extension curves for fibers pulled below 40 pN at room temperature.
Fibers with LHs (fixed or dynamic) are simulated in high monovalent
salt (0.150 M NaCl) and low concentration of magnesium ions. Fibers
without LH are simulated in high monovalent salt only. The curve
labels show the average LH–core bond concentration in each binding
regime; such concentrations are obtained with the binding probabilities
given in Table 1. The force–extension curve is a plot of the magnitude
of the applied force versus the ‘end-to-end’ extension or distance (in the
direction of the stretching force) between the geometric centers of the
first and last nucleosome cores. Error bars in the force–extension curve
denote the standard deviation from the mean of the ensemble average.
Dynamic LH binding dramatically reduces LHs stiffening effect and
more so as the LH–core binding affinity decreases.
Consequently, such parameters yield equilibrium
ensemble values of oligonucleosomes in which the
majority of LH proteins (80%) are bound to cores. On
the other hand, probability combinations with Pa < Pd
describe a low LH-core binding affinity and yield chromatin fibers with a reduced number of LH–core bonds.
Table 1 also indicates that the individual conformations
in the ensemble have a LH-core bond concentration that
deviates 10% from the mean, reflecting a fluctuation in
the number of LH-core bonds consistent with dynamic
regimes.
The force–extension curves in Figure 2b demonstrate
marked differences between fibers with fixed LHs (red
curve), dynamic LHs (green, turquoise, purple and
magenta curves), and no LH (blue curve). Note that all
dynamic-LH curves lie between the two extreme cases
(fixed-LH, red and no-LH, blue). Fibers without LH
(blue curve) require only 2 pN to produce a 2-fold extension from their resting length (equilibrium fiber length at
zero pulling force; values given in Table 1). In comparison,
Nucleic Acids Research, 2012, Vol. 40, No. 18 8809
Table 2. Force-extension slope during two force regimes
Fiber
Dynamic LH (effective diffusion)
Fixed LH
No LH
Straightening regime
Unfolding regime
Force (pN)
Slope ± SD (pN/nm)
Force (pN)
Slope ± SD (pN/nm)
0–6
0–25
–
0.1211 ± 0.0624
0.4478 ± 0.0966
–
>6
>25
<4
0.0319 ± 0.0089
0.0611 ± 0.0160
0.01077 ± 0.0005
Fibers with LHs were modeled in high monovalent salt and low concentration of magnesium ions. Fibers without LH were modeled in high
monovalent salt only.
the force needed to double the resting length of fixed-LH
fibers (red curve) is well above experimental values (21,26),
reaching 25 pN; these fibers are extremely stiff.
By considering dynamic-LH binding/unbinding, we
observe a dramatic reduction of fiber stiffness. The
forces needed to double the resting length of fibers with
dynamic LH–core bonds approach the no-LH value as
the binding affinity decreases; for example, the forces for
high, moderate, and low affinities are 4.5, 4, and 3 pN,
respectively. Even for dynamic-LH fibers with the
highest binding affinity considered (effective diffusion
case), we observe a remarkable softening with respect to
fixed-LH fibers: the force needed to double their resting
length is only 6 pN (compared with 25 pN for fixed-LH
species).
The high stiffness of fixed-LH fibers results from the
presence of magnesium ions and the formation of rigid
DNA stems—209-bp chromatin with fixed-LH in monovalent salt only doubles its resting length at a much lower
value, 10 pN (17). Divalent ions increase chromatin stiffness significantly by (i) bending the DNA linkers and
screening the DNA–DNA repulsion, which allows the nucleosomes to come closer together, and (ii) permitting the
nucleosome cores to rearrange in a wider range of conformations that yield optimum contacts within an
extended array; both effects favor strong internucleosome
interactions and make unfolding more challenging. Rigid
DNA stems further screen DNA repulsion and lock the
chromatin fiber in a compact form. This observation
suggests that DNA stems and divalent ions work
together to stabilize chromatin compaction, increasing
the forces needed to unfold the fiber.
Dynamic LH with high binding affinity
In the remainder of this article, we elaborate upon the
behavior of fibers with LHs that exhibit effective diffusion
(highest binding affinity) by comparing it with that of
fibers without LH and with fixed LHs. Hereafter, we
refer to the fibers with LH molecules that display effective
diffusion as ‘dynamic-LH fibers’. Results from this regime
are the most relevant biologically because the majority of
LH molecules are bound to cores, as in vivo (10).
Softening caused by this dynamic-LH binding behavior
can also be noted by comparing the slopes of the force–
extension curves. In Figure 2b, separate regimes (force
ranges), in which the force–extension curves of fixed-LH
(red curve), dynamic-LH (green curve), and no-LH (blue
curve) fibers present linear extension behavior individually, can be recognized. For each fiber, the force regimes
can be distinguished by their different slopes; the slope
quantifies the fiber’s propensity to extend during such
regime. The forces at which these regimes occur and the
corresponding slopes of the force–extension curves are
shown in Table 2.
Fibers with fixed and dynamic LHs display two separate
force regimes. The slopes in both regimes are much
smaller for dynamic-LH fibers than for the rigid
fixed-LH arrays. In the first force regime, both curves
have their largest slopes, which suggests that the fibers
straighten and then open partially, maintaining their
original zero-force structure. During the second force
regime, the slopes drastically decrease; a small force
increase now produces a notable fiber extension, signaling
fiber unfolding. The slope for dynamic-LH fibers in this
second force regime is 0.03 pN/nm, in excellent agreement with the 0.02–0.028 pN/nm values estimated for
medium-NRL chromatin with magnesium ions (26).
In comparison, the force–extension curve of no-LH
fibers shows three different force regimes. Instead of an
initial straightening regime, the fiber unfolds (minimum
slope) and the force–extension curve resembles a
plateau; the slope in this regime is six times smaller than
that for fixed-LH fibers (Table 2). A similar plateau at low
forces was previously reported by Cui and Bustamante
(21) for medium-NRL chromatin at low salt, where a
loose structure is expected. At intermediate forces, the increased slope suggests reorganization into a stiffer structure. At high forces, nonlinear behavior due to DNA
over-stretching occurs. This fiber is further analyzed
in (17).
To further quantify chromatin’s stiffness, we estimate
the stretching elasticity modulus s, defined as the force
needed to produce a 2-fold extension (71). Fixed-LH
fibers show a stiff elasticity modulus of s & 25 pN, close
to values calculated by Aumann et al. (40) for fibers with
rigid DNA stems. In comparison, the softer dynamic-LH
fibers have an elastic modulus of s & 6 pN, in agreement
with the s = 5–8 pN experimental values (21,72). This remarkable stiffness reduction (by a factor of almost 5)
caused by LHs dynamic binding behavior demonstrates
that LH mobility plays an important role in facilitating
force-induced chromatin unfolding.
Note that our force–extension curves mimic the
behavior of integral chromatin fibers, i.e. fibers in which
all nucleosomes remain intact; the effects of nucleosome
unwrapping and sliding are not included in our model.
Experiments indicate that the presence of histone
variants and post-translational modifications throughout
the dyad DNA entry/exit region can induce nucleosome
8810 Nucleic Acids Research, 2012, Vol. 40, No. 18
unwrapping even at zero force (73). For instance, H3
lysine 56 is located in the dyad region and its acetylation
encourages transient nucleosome unwrapping (74). Some
remodeling complexes also function by favoring nucleosome unwrapping. For example, the SWI/SNF complex is
thought to strip off a section of DNA around the dyad
position (75). It has been speculated that nucleosome
unwrapping creates a DNA bulge on the nucleosome
surface close to the dyad that propagates sliding the
cores (76), and as such might increase the degree of
positional delocalization (or ‘fuzziness’) of nucleosomes
across the genome (77). In addition, modeling of
medium-NRL chromatin without LH and without
divalent ions has suggested that in native nucleosomes
unwrapping becomes significant above 4.5 pN (44).
We expect individual nucleosome unwrapping to
modify the electrostatic properties of the partially
unwrapped cores. Multiple transient nucleosome unwrappings and enhanced fuzziness might favor fiber compaction and fiber stiffening. Note, however, that for the
conditions analyzed here (divalent ions and LHs), the effects of nucleosome unwrapping and sliding are expected
to be reduced because experiments show that unwrapping
in divalent ion conditions occurs only at high forces
[>15–25 pN, approximately (22,23)] and that LHinduced stems restrict nucleosome movement. Consistently, other experiments have also found that, in the
presence of magnesium ions, chromatin unfolds by initially forming an open beads-on-a-string structure with
most internucleosome contacts broken and no unwrapped
nucleosomes (26).
Unfolding mechanism of chromatin with dynamic LHs
To describe how the internal organization of nucleosomes
in the chromatin fiber changes with the pulling force, we
complement the force–extension curves with an analysis of
representative simulation snapshots and internucleosome
interaction patterns (32,34) (Figure 3). These patterns
measure the relative intensity of histone-tail mediated
interactions between nucleosomes separated by k neighbors (i ± k). For example, dominant i ± 2 contacts are
indicative of a compact two-start conformation (the
zigzag), while dominant i ± 1 and i ± 6 interactions
suggest a 6-nucleosomes-per-turn solenoid model (34).
The combined information in Figure 3 reveals different
fiber opening mechanisms. For dynamic-LH fibers (left
panels), we have the following steps: (i) within 0–6 pN,
the fiber straightens while maintaining a zigzag organization with DNA stems (dominant i ± 2 and moderate i ± 5
contacts) (ii) within 7–12 pN, individual linker-DNA
stems rupture, causing significant fiber extension and
yielding partially unfolded heteromorphic structures we
term ‘superbeads-on-a-string’; these structures combine
stretched fiber regions with ‘superbeads’, or compact
zigzag clusters, in which the nucleosomes interact
strongly with their zigzag neighbors (i±2) and moderately
with other cores (i±1 and i±3); (iii) between 13 and
16 pN, the DNA stems continue to break reducing the
presence of superbeads and their intense i±2 contacts;
(iv) at 16 pN, most DNA stems have ruptured and
the fiber forms a distinctive ‘single-stack’ conformation
with dominant i±1 interactions; the nucleosomes in this
structure are vertically aligned, but instead of stacking
parallel on top of one another, they are irregularly
oriented to maximize the strength of i±1 interactions;
and (v) above 16 pN, the single-stack fiber stretches to
form an open beads-on-a-string conformation with negligible internucleosome interactions.
Unfolding of fixed-LH fibers (middle panels) proceeds
though the same five steps described above for
dynamic-LH fibers. However, the forces needed to
initiate each unfolding step are much higher when LHs
are fixed due to destabilization of the rigid DNA stems
and an enhanced configurational heterogeneity. Indeed,
dynamic-LH DNA stems start rupturing above 6 pN
compared with fixed-LH stems at only 25 pN. These
forces coincide with those at which the force–extension
slopes change, confirming that these slope changes signal
structural transitions.
Without LH (panels at right), the three force regimes
correspond to conformations of irregular opening,
single-stack, and unfolded chain, respectively. In the
single-stack organization (4–10 pN), the parallel alignment
of nucleosomes facilitates optimum internucleosome interactions and explains the higher resistance to stretching
(increased slope) in this force range. Although for fibers
without LH this transition into a single-stack conformation coincides with an increased force–extension slope,
for fibers with dynamic and fixed LH this transition
does not alter the shape of the force–extension curve
and is revealed only by our simulation analysis. This different correlation between the slope change and actual
conformational transition shows that the interactions
between immediate nucleosomes, which stabilize the
single-stack conformation, stiffen the fiber without LH
at low forces (4–10 pN) but can be ruptured easily at
higher forces (16 and 36 pN for dynamic and fixed LH,
respectively). Notably, these single-stack conformations
emerge for simulations started from zigzag fibers and are
not evidence of an initial solenoid fiber organization (26).
This underscores the utility of modeling to extract structural information from stretching experiments.
Formation of superbeads-on-a-string intermediates is
observed for all fibers in divalent conditions, regardless
of LH binding rate (see representative snapshots in
Supplementary Figure S2). In contrast, in fibers without
LH and without divalent ions, formation of such structures is negligible. Stabilization of these structures requires
the presence of LHs and divalent ions to decrease DNA–
DNA repulsion, increase DNA bending, and bring the
nucleosomes in closer contact inside compact clumps.
This is consistent with the observation that chromatin
fibers with LHs and divalent ions are heteromorphic and
exhibit zigzag features of straight linker DNA combined
with moderate DNA bending (19).
The stability of superbeads-on-a-string structures in the
presence of LHs and divalent ions is supported by several
experimental observations. First, stable structures
combining unfolded fiber regions and small aggregates
of nucleosomes have been visualized by atomic force microscopy of trypsin-digested chromatin with LHs and
Nucleic Acids Research, 2012, Vol. 40, No. 18 8811
(a), (b)
(c)
Figure 3. Effect of dynamic LH binding on chromatin’s unfolding mechanism, as characterized by (a) force–extension curves, (b) patterns of
internucleosome interactions, and (c) simulation snapshots (space filling models in which alternating nucleosomes are colored white and navy,
DNA as red and LH turquoise). The three vertical panels are for 24-core 209-bp oligonucleosomes at 0.15 M monovalent salt with: dynamic LH
and Mg2+ (with Pa=1 and Pd=0.25), fixed LH and Mg2+, and no LH and no Mg2+ (green, red, and blue curves in Figure 2, respectively). These
snapshots are presented for different force regimes: low (yellow background), moderate (blue background), high (pink background) and very high
(purple background). Some longer structures are only shown partially at bottom, as denoted by three dots. Fibers with dynamic LHs unfold via
superbeads-on-a-string (SBS) structures at much lower forces than fibers with fixed LHs.
magnesium ions (36). This is relevant to our study because
trypsin digestion removes the N-terminal histone tails and
triggers an equivalent effect to that of applying a pulling
force: inducing fiber unfolding (78). Second, electron microscopy of digested chromatin fibers with NRLs of 200
and 212 bp, both with LHs and in high monovalent salt,
has already revealed the formation of regular clumps of
nucleosomes, or superbeads, measuring 32 and 35 nm, respectively (35). Simple estimation in our chromatin snapshots indicates similar dimensions (see green lines in
Figure 3). Animations of the three unfolding mechanisms
are available on http://www.biomath.nyu.edu/index/
gallery.html.
Internucleosome interaction energy during fiber unfolding
The folded state of the chromatin fiber is stabilized by
electrostatic interactions between the positively charged
and flexible histone tails, which extend from the nucleosome surface, and the charged surfaces of neighboring
cores. During force-induced stretching, this stabilizing
internucleosome interaction energy must be overcome
before the fiber unfolds. Figure 4 plots this energy as a
function of the pulling force. We define this energy as the
average nucleosome/nucleosome electrostatic interaction
energy per core, considering all nucleosome charges in
the surface and histone tails.
The maximum strength of the stabilizing internucleosome interaction energy occurs at zero pulling
force, when the fiber is most compact. Fibers without
LH have a loose zero-force structure stabilized by a
low internucleosome energy of 1 kbT (i.e. mean energy
per core ± standard deviation: 1.03 ± 0.11 kbT). Fibers
with fixed and dynamic LHs have compact structures in
the absence of pulling force maintained by internucleosome energies of 5 kbT (i.e. Fixed LH = 5.04 ± 0.21
kbT and dynamic LH = 4.72 ± 0.26 kbT). Equilibrium
data in Supplementary Figure S3 confirm these compaction trends. Internucleosome energies of 1 kbT and 5 kbT
for loose and compact chromatin, respectively, are reasonable, considering that a value of 3 kbT has been
determined for medium-NRL fibers with LHs in the
absence of magnesium ions, where fibers are expected to
be moderately compact (21,29). Our internucleosome
energy for compact chromatin is weak when compared
with the 14 kbT estimate for 197-bp fibers with LHs
and magnesium ions (26). However, as recently challenged
by Lavelle et al. (79), such a high internucleosome energy
was derived assuming a solenoid conformation and a
model with five variable parameters. Although a high 14
kbT internucleosome interaction energy is necessary to stabilize a solenoid arrangement with highly bent linkers and
strong DNA–DNA repulsion, a weaker 3 kbT-value can
maintain a zigzag fiber with straight linkers (29). Our
8812 Nucleic Acids Research, 2012, Vol. 40, No. 18
experiments (19,34); and force–extension behavior in
monovalent salt conditions (17).
A comparison of chromatin force–extension curves
from different studies is complex because the results are
highly sensitive to the experimental conditions; importantly, the many studies available analyze chromatin
fibers of different characteristics (e.g. NRL, number of
nucleosomes, and LH presence/absence) and under
varying experimental conditions (e.g. ionic environment
and applied forces). Thus, no single chromatin force–
extension experimental or modeling benchmark exists.
Nonetheless, here we plot our results together with
selected available data to interpret general trends.
In Figure 5, we compare our force–extension curves
with experimental and modeling studies of mediumNRL chromatin fibers (190–210 bp). Given that the
end-to-end equilibrium extension is correlated with
the number of cores in the chromatin fiber, to facilitate
the comparison in Figure 5, we plot the force versus the
extension-per-core. Considering the expected effects of
the different conditions used in each study, the figure
confirms that our simulated curves are consistent with
previous works.
Figure 4. Top: internucleosome interaction energy per nucleosome
versus force for 24-core 209-bp oligonucleosomes at 0.15 M monovalent salt: fixed LH and Mg2+ (red) and dynamic LH and Mg2+ (green),
versus no LH and no Mg2+ (blue). Error bars denote the standard
deviation from the mean of the ensemble average. For visualization
purposes, the low-force–low-energy region is expanded on the right.
Bottom: space-filling models based on MC simulations of fibers with
dynamic LHs and Mg2+ show DNA in red and alternating nucleosomes
in white and blue. The zero-force energy is similar for fibers with fixed
and dynamic LHs. The different force regions in which the curve with
dynamic LHs has a constant slope correspond to: (1) low force where
compact zigzag fibers form; (2) moderate force where superbeadson-a-string arrangements occur; (3) high force where a one-start structure is stable and (4) very high force where a fully extended array forms
with no internucleosome interactions (zero energy).
intermediate internucleosome energy of 5 kbT agrees well
with the compact hetermorphic chromatin structure
observed in divalent conditions, which combines straight
and bent DNA linkers (19).
Comparison with previous modeling and experimental
works
Our integrated chromatin coarse-grained model has been
extensively validated against different available experimental data (32,34). In past work, we have shown that
our model reproduces the following experimental results:
salt-dependent sedimentation coefficients and packing
ratios of 12-unit oligonucleosomes of chicken erythrocyte
chromatin over a broad range of monovalent salt concentrations, with/without magnesium ions, and with/without
LHs (32); diffusion and salt-dependent behavior of mononucleosomes, dinucleosomes, and trinucleosomes (30);
salt-dependent extension of histone tails (30); the irregular
zigzag and solenoid topologies of chromatin fibers (29,34),
and their enhanced compaction upon LH binding (32,34);
linker crossing orientations (32); internucleosome interaction patterns consistent with cross-linking and EM
Fixed-LH curve
Our stiffer fixed-LH curve lies closely below to that of
no-LH fibers modeled by Aumann et al. (40). Even
though Aumann’s fibers were simulated in the absence
of LH (a softening factor), their relatively high stiffness
can be explained by their much shorter NRL (190 bp
versus 209 bp in our work). Decreased NRLs have been
shown to significantly stiffen the chromatin fiber
(17,26,40), because they hinder reorganization into
extended arrays and favor intense internucleosome interactions (17).
No-LH curve
At low forces (<4 pN, see figure inset), the force–extension
curve of our no-LH fibers lies closely above that of no-LH
fibers simulated by Kepper et al. (44). This low force range
is most relevant for analyzing unfolding behavior of our
no-LH fibers, given that all but some i±1 internucleosome
interactions are broken above such force. Compared
with our arrays, the Kepper fibers have a slightly shorter
NRL (199 bp versus 209 bp in this work) but were
simulated at lower monovalent salt concentration
(0.10 M NaCl versus 0.15 M in this work); these differences produce competing stiffening and softening effects
in the stretching response, and explain the similitude
between curves. This agreement supports both modeling
approaches, which consider different approximations but
nonetheless yield similar chromatin behavior. At low
forces, our no-LH curve is also consistent with the experimental curve for 210-bp fiber of Cui and Bustamante (21).
Although Cui and Bustamante’s curve is for chromatin
with LHs, this curve is only moderately stiffer than our
no-LH result because the former was handled at lower
monovalent salt concentration (0.04 M NaCl versus 0.15
M in this work), which produces fiber loosening (34)
similar to that observed in the absence of LH. At low
forces, our no-LH curve also runs under the no-LH
Nucleic Acids Research, 2012, Vol. 40, No. 18 8813
Figure 5. Comparison of our results with previous experimental (Exp.) and modeling (Mod.) force–extension curves. Bottom: force-extension curves
of the various works. Top: low-force region expanded for visualization purposes. Results from this work are shown in solid lines (red = fixed LH,
green = dynamic LH with Pa=1 and Pd=025, blue = no LH), results from other works are shown in dashed lines. The references and
experimental/modeling conditions for each work are summarized in the legend. Data shown for other works has been taken directly from the
different paper figures. For comparison purposes, instead of the extension, the extension-per-core (extension divided by the total number of cores) is
used.
curve of Kruithof et al. (26); this is also reasonable
because the experimental fibers have a slightly shorter
NRL (197 bp) and, unlike our no-LH fibers, were
manipulated in the presence of magnesium ions, which
induce compact folding and fiber stiffening. Considering
the effects of nucleosome unwrapping might be important
to model behavior of these no-LH fibers without divalent
ions at higher forces (>4 pN).
Dynamic-LH curve
Our dynamic-LH fiber has an intermediate stiffness
between the extremes of fixed-LH and no-LH curves. As
expected, it is softer than Aumann’s 190-bp fiber (40)—
consistently with softening induced by longer NRLs
(17,26,40)—and stiffer than the low-salt fiber of Cui and
Bustamante (21) and the no-LH fibers of Kepper et al.
(44) and Kruithof et al. (26). Moreover, our results
offer an explanation to Kruithof’s observation that LH
molecules do not affect the stiffness of the chromatin
fiber: as shown in Figure 2, fibers with highly mobile
LH molecules (low affinity) can exhibit the same stiffness
as fibers without LH. High LH mobility is consistent with
the experiment because the strain induced in the fiber by
the stretching process can destabilize the LH–core bonds.
CONCLUSIONS
Our suggestion for a critical role for dynamic linker
histone binding/unbinding during force-induced chromatin fiber unfolding at divalent ion conditions is based
on analyses of the force–extension curves, internucleosome interaction patterns, simulation snapshots, and
internucleosome energy. These data also indicate that
(i) fixed-LH DNA stems require forces >25 pN to break;
(ii) dynamic-LH binding/unbinding behavior destabilizes
the rigid DNA stems, reducing dramatically chromatin’s
stiffness (stretching modulus) and the forces needed to
initiate unfolding to 6 pN; (iii) in the presence of
divalent ions and LHs, chromatin unfolding proceeds
through irregular superbeads-on-a-string intermediate
structures that combine fully extended DNA regions
8814 Nucleic Acids Research, 2012, Vol. 40, No. 18
with compact clumps; (iv) compact chromatin fibers with
LHs and divalent ions are stabilized by an average
internucleosome interaction energy of 5 kbT, consistent
with a heteromorphic structure; and (v) zigzag fibers
adopt a single-stack structure just before unfolding into
a beads-on-a-string array. As discussed below, these observations have important biological implications.
Although related softening due to dynamic-LH binding
and heteromorphic intermediates emerged from our recent
work with monovalent ions only (17), our present work
suggests the important role of divalent ions and provides
further insights into chromatin unfolding at physiological
conditions. First, the added compaction introduced by
divalent ions is not sufficiently strong to eliminate, or substantially attenuate, the dramatic softening produced by
dynamic, compared with static, LH binding. Second,
divalent ions induce unfolding through heteromorphic
superbeads-on-a-string intermediates in all LH binding
modes examined. In particular, such conformations
appear in fibers with low affinity LH–core bonds, unlike
the case for monovalent ions (17).
The heteromorphic superbeads-on-a-string structures
have characteristics and dimensions similar to those of
experimentally observed chromatin lumps (35,36). Such
structures might be important for gene regulation, as
they selectively expose certain regions of the genome and
maintain others protected inside compact clumps. The
global stability of superbead structures in vivo depends
on the ability of divalent ions to screen repulsion among
DNA linkers, enhance DNA bending, and accommodate
multiple internucleosome interactions (19). In addition,
LH binding at a specific DNA entry/exit point would
further screen the DNA linker repulsion locally.
Therefore, modulation of the LH–core binding affinity,
across a fiber, by post-translational modifications of LH
and its binding sites (9,80) suggests a mechanism to guide
the superbead and stretched segment locations and control
DNA access. Thus, the combined effects of LH mobility
and DNA bending might play a role for gene regulation
through stabilization of softer fiber arrangements accessible to molecular motors and unfolding through heteromorphic conformations that facilitate selective DNA
expression.
These superbeads-on-a-string structures may also represent transitional states between different chromatin forms
present at the various stages of the cell cycle. During
cell-cycle progression, chromatin structure suffers large
modifications that lead the dynamical changes in gene expression (81). In addition, modifications of chromatin
structure during the cell cycle could act as signals to
activate checkpoint pathways (82). It has also been suggested that chromatin structural changes could contribute
to DNA repair itself, by facilitating lesion accessibility
(82); which is consistent with chromatin transitioning
between forms through superbeads-on-a-string structures.
Thus, the high heterogeneity we observe in partially
unfolded/transitional chromatin might indicate that
divalent ions and dynamic LHs are essential facilitators
of the chromatin structural plasticity required to trigger
and signal vital cell-cycle events.
The dramatic softening of fiber resistance to pulling by
dynamic-LH binding in divalent conditions provides a
novel explanation to two surprising recent observations:
that (i) the experimental force–extension curves of fibers
with and without LH are equivalent at low forces when
magnesium ions are present (26), and (ii) transcription
occurs within chromatin fibers non-uniformly compacted
above the 30-nm chromatin level (83). Indeed, our results
suggest that transcribed chromatin would be unfolded
locally, by the pulling force generated by RNA polymerase to allow transcription, but remain compact at distal
gene segments.
Fiber softening correlates with unfolding at lower
forces. This force reduction might be crucial as eukaryotic
molecular motors that operate in chromatin, function
within the low force range in which dynamic-LH fiber
unfolding is observed in this work. For instance, a
single-molecule study revealed that RNA polymerase II
ceases to transcribe at 7.5 ± 2 pN (compared with 35 pN
for its prokaryotic counterpart) or at 16.9 ± 3.4 pN in the
presence of TFIIS, a transcription elongation factor that
facilitates transcription (70). In addition, FRAP experiments suggest that the globular and C-terminal domains
of H1 form the LH-chromatin bound state through alternative pathways involving several different partially
bound intermediates that are susceptible to competition
by other binding factors (10). Hence, LH dynamic
binding/unbinding, together with binding factors might
provide the opportunity for molecular motors to achieve
chromatin stretching and gain access to the DNA at
natural forces without disrupting the global chromatin
organization.
Furthermore, during gene expression, the mechanical
constraints induced in the fiber structure by the pulling
machinery may destabilize the LH–core bound state,
enhancing LH mobility. Enhanced LH mobility in the
presence of mechanical constraints is consistent with an
optical tweezers experiment of chromatin with LH B4; it
suggests that, during force-induced stretching, the LH–
core bond is broken before nucleosome disruption
occurs (24). Enhanced LH mobility may in fact distinguish
active from silent chromatin and constitute a necessary
factor to trigger fiber unfolding.
Finally, our modeling snapshots and internucleosome
patterns confirm that zigzag fibers unfold through a
single stack conformation. A single-stack is thus not
evidence for a solenoid structure (26). The solenoidal explanation in (26) is based on the observation that 197-bp
arrays stretch with a constant slope up to a maximum
length which is consistent with a regularly folded single
stack of perpendicular nucleosomes and on the assumption that a zigzag fiber is associated instead with a shorter
two-stack structure. As we observe, however, zigzag fibers
with LHs conserve the force–extension slope past the
two-stack size limit. The unfolding process could be
further attenuated by the ability of the nucleosomal
DNA to transiently peel-off the histone core. As discussed
in Lavelle et al. (79), the experiments in (26) have already
been re-interpreted to support a zigzag organization (79).
The results presented here suggest a fascinating biological feature to regulate fiber structure and hence DNA
Nucleic Acids Research, 2012, Vol. 40, No. 18 8815
accessibility, cell-cycle progression, and cell-cycle checkpoints, by divalent ions effects and a dynamic LH
binding/unbinding mechanism. The possible crucial role
that dynamic LH binding has in facilitating transient
chromatin unfolding also underscores the importance of
considering the highly dynamic nature of chromatin to
decipher the external and internal factors that drive and
alter gene expression. Recent data suggest that the pulling
force created during transcription may organize the global
architecture of an extended chromosomal domain in situ
(84). Other architectural factors may include HMG
proteins that accelerate LH mobility (9) or chromatincondensing proteins such as HP1 (85) and MENT (86)
that may polymerize on the nucleosomes to inhibit transient unfolding of the chromatin fiber. Together with other
variables that affect chromatin compaction and configurational transitions, such proteins suggest how small local
differences can have profound global effects.
SUPPLEMENTARY DATA
Supplementary Data are available at NAR Online:
Supplementary Table 1, Supplementary Figures 1–3 and
Supplementary Methods.
ACKNOWLEDGEMENTS
The authors thank Dr Sergei Grigoryev for his invaluable
comments and insights concerning this work. Computing
support from the NYU HPC USQ and Cardiac clusters is
also acknowledged.
FUNDING
National Science Foundation [MCB-0316771 to T.S.];
National Institutes of Health (NIH) [R01 GM55164 to
T.S.]; American Chemical Society [PRF39225-AC4];
Petroleum Research Fund (to T.S.); Philip Morris USA
(to T.S.); Philip Morris International (to T.S.);
Schlumberger Faculty for the Future Program (to R.C.-G.).
Funding for open accees charge: National Science
Foundation [MCB-0316771 to T.S.]; NIH [R01
GM55164 to T.S.].
Conflict of interest statement. None declared.
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